2.2.1 Central Composite Designs
Central composite designs (CCDs) are built from factorial 2
k - or fractional factorial
2
k-n -designs. Additionally, center and star points (marked gray) are augmented,
allowing the estimation of curvature. In general, three variations of CCD exist,
which differ in range settings of their factors. Figure 1 C–E illustrates the relationships among these variants. Depending on the variant, the design is spherical,
orthogonal, rotatable, or face centered [28, 38, 42].
2.2.2 Box-Behnken Designs
Box-Behnken designs (BBDs; see Fig. 1f) are based on the combination of a
two-level factorial design with a balanced incomplete or partial block design
[43]. They are nearly rotatable and require an examination on three levels for each
factor, resulting in a field with distinct resolution of interactions and quadratic effects
[44]. However, for a large number of factors, this implies a poor estimation of the
two-factor interactions [43].
2.2.3 Optimal Designs
With optimal experimental designs, the experimental space can be restricted, and
user-specific settings can be made. There are a large number of optimization criteria
to distribute points in the experimental space. The most frequent representatives are
average (A)-, determinant (D)- (shown in Fig. 1g), eigenvalue (E)-, global (G)-, and
variance (I)-optimality. If the coefficients of the regression model are of interest, then
A-, D-, and E-optimal plans are used. G- and I-optimality, however, refer to the fitted
regression model [38].
2.2.4 Space-Filling Designs
Traditional experimental designs, such as the CCDs, BBDs, and the optimal experimental designs, often create experiments close to the factor boundaries. This can
cause areas of free space, which are not examined and only minimize noise
[45]. However, to minimize bias, space-filling designs can be used. In this case,
possible experiments are randomly distributed in the individual spaces. An example
of such designs is the Latin Hypercube Sample Design (LHSD), which fills the room
evenly, allowing for a large number of factors and levels to be used (Fig. 1h). The
experimental space is filled in such a way that there is an even distribution in the
entire factor space or the maximum distance between the design points is minimized.
However, the corners of the factor space are left out obtaining this information would
only be possible by extrapolation [41, 46].
36
K. B. Kuchemüller et al.
Central composite designs (CCDs) are built from factorial 2
k - or fractional factorial
2
k-n -designs. Additionally, center and star points (marked gray) are augmented,
allowing the estimation of curvature. In general, three variations of CCD exist,
which differ in range settings of their factors. Figure 1 C–E illustrates the relationships among these variants. Depending on the variant, the design is spherical,
orthogonal, rotatable, or face centered [28, 38, 42].
2.2.2 Box-Behnken Designs
Box-Behnken designs (BBDs; see Fig. 1f) are based on the combination of a
two-level factorial design with a balanced incomplete or partial block design
[43]. They are nearly rotatable and require an examination on three levels for each
factor, resulting in a field with distinct resolution of interactions and quadratic effects
[44]. However, for a large number of factors, this implies a poor estimation of the
two-factor interactions [43].
2.2.3 Optimal Designs
With optimal experimental designs, the experimental space can be restricted, and
user-specific settings can be made. There are a large number of optimization criteria
to distribute points in the experimental space. The most frequent representatives are
average (A)-, determinant (D)- (shown in Fig. 1g), eigenvalue (E)-, global (G)-, and
variance (I)-optimality. If the coefficients of the regression model are of interest, then
A-, D-, and E-optimal plans are used. G- and I-optimality, however, refer to the fitted
regression model [38].
2.2.4 Space-Filling Designs
Traditional experimental designs, such as the CCDs, BBDs, and the optimal experimental designs, often create experiments close to the factor boundaries. This can
cause areas of free space, which are not examined and only minimize noise
[45]. However, to minimize bias, space-filling designs can be used. In this case,
possible experiments are randomly distributed in the individual spaces. An example
of such designs is the Latin Hypercube Sample Design (LHSD), which fills the room
evenly, allowing for a large number of factors and levels to be used (Fig. 1h). The
experimental space is filled in such a way that there is an even distribution in the
entire factor space or the maximum distance between the design points is minimized.
However, the corners of the factor space are left out obtaining this information would
only be possible by extrapolation [41, 46].
36
K. B. Kuchemüller et al.